Napoli travelled to the Stadio Olimpico knowing another reverse could hamper their bid for a third-place finish.
Still smarting from their Italian Cup exit at the hands of Juventus in midweek, Napoli travelled to the Stadio Olimpico knowing another reverse could hamper their bid for a third-place finish.
But Napoli were unbeaten away to Lazio since a 3-1 league loss in April 2012, and, after seeing Sergej Milinkovic-Savic go close with two early efforts for the hosts, were off the mark on 25 minutes when Spain forward Callejon finished off a great passing move between Marek Hamsik and Dries Mertens.
Insigne was completely unmarked when he somehow fired wide from Mertens' through ball before the half-time interval.
But the Italy midfielder made amends six minutes after the restart when he met Allan's chipped pass to prod into the far bottom corner from a tight angle.
Amid a late Lazio onslaught, Napoli coach Maurizio Sarri replaced Callejon with midfielder Piotr Zielinski and the move paid off, the Pole cushioning Arkadiusz Milik's cross for Insigne to sweep home his second in stoppage time.
Napoli remain third, and although four points behind Roma in the second automatic Champions League spot, the southerners -- who lost their Cup semi to Juve 5-4 on aggregate in midweek -- have cast Lazio seven points adrift.
"The lads could have paid for their efforts in midweek against Juventus, but they didn't," said Sarri, who was quick to underline they had beaten the champions 3-2 in the Cup last week, days after a 1-1 league draw at the San Paolo.
"In three days we held Juve 1-1 and beat them in the Cup, and that's not too bad.
"Tonight the lads gave me the right response. Let's keep going, and get as many points as possible."
Simone Inzaghi's Lazio, in fourth, hold a one-point lead on Atalanta, whose unlikely push for a Europa League spot was given a boost when Inter Milan were stunned 2-1 at Crotone.
A week after a 2-1 home defeat to Sampdoria extinguished their Champions League qualifying hopes, Inter's chances of even qualifying for the Europa League are hanging by a thread after Diego Falcinelli hit a dramatic first-half brace in Calabria, where Danilo D'Ambrosio reduced the arrears in the 65th minute.
Inter's 10th league loss comes a week before the Milan derby, but after the "heavy defeat", coach Stefano Pioli told Sky Sport: "It would be too easy to apologise to the fans. We now have to go out and show that today was just a blip."
Crotone remain third from bottom but Davide Nicola's men are now just three points from the safety zone.
As Inter floundered, AC Milan had Suso, Mario Pasalic, Carlos Bacca and Gerard Deulofeu to thank for the goals in a solid San Siro display that moved the Rossoneri up to sixth place, two points behind Atalanta.
Coach Vincenzo Montella hailed his side's "aggressive" performance and secretly hopes Inter's recent woes persist.
"The derby is a game apart. You don't even take each sides' technical ability into consideration," said Montella.
"Even the last time we met, Inter were going through a tough period. But it will be a difficult game."
Juventus had moved nine points clear with a 2-0 win over Chievo on Saturday, when Gonzalo Higuain hit his second brace in as many outings, but Roma restored their six-point deficit with a confident 3-0 win at Bologna thanks to goals from Federico Fazio, Mohamed Salah and Edin Dzeko .
Dzeko is now joint top of the Serie A scoring charts on 24 goals, with Torino marksman Andrea Belotti.
Belotti struck once in a 3-2 defeat at Cagliari, who saw Han Kwang-Song strike in the 95th minute to become the first North Korean to hit the back of a Serie A net.